1. **State the problem:** Rhianna wants to invest 50000 at an interest rate compounded semiannually to have 65000 in 4 years. We need to find the rate per year compounded semiannually. 2. **Identify known variables:** - Principal, $P = 50000$ - Amount after 4 years, $A = 65000$ - Time, $t = 4$ years - Compounding frequency, semiannual means $n = 2$ times per year 3. **Use compound interest formula:** $$ A = P \left(1 + \frac{r}{n}\right)^{nt} $$ where $r$ is the annual interest rate (decimal form), and we want to find $r$. 4. **Substitute known values:** $$ 65000 = 50000 \left(1 + \frac{r}{2}\right)^{2 \times 4} = 50000 \left(1 + \frac{r}{2}\right)^8 $$ Divide both sides by 50000: $$ \frac{65000}{50000} = \left(1 + \frac{r}{2}\right)^8 $$ $$ 1.3 = \left(1 + \frac{r}{2}\right)^8 $$ 5. **Take the 8th root:** $$ \left(1 + \frac{r}{2}\right) = 1.3^{\frac{1}{8}} $$ Calculate $1.3^{\frac{1}{8}}$: $$ 1.3^{\frac{1}{8}} \approx 1.0335 $$ 6. **Solve for $r$:** $$ 1 + \frac{r}{2} = 1.0335 $$ $$ \frac{r}{2} = 0.0335 $$ $$ r = 0.067 $$ Convert to percentage: $$ r = 6.7\% $$ 7. **Conclusion:** The closest option to 6.7% is **6.68%**. **Final answer:** Rhianna should invest her money at **6.68%** compounded semiannually to accumulate 65000 in 4 years.